SORROW AND ADVERSITY 191 



sert that the logic of philosophy has a mathematical 

 basis, but to suggest that the Hegelian dialectic ad- 

 mits of geometrical demonstration is venturing far 

 into the borderland of the bizarre. 



However, I believe to have discovered therein a 

 four-dimensional solution of life's problems. For our 

 three-way vision, reality is divided into two parts. 

 Now it is the one that seems illusion, now the other, 

 as the light chances to fall. The human mind has 

 laboured in vain with the problem of opposites for the 

 very want of the higher synthesis afforded by the 

 four-dimension concept. And so it has gone on from 

 century to century alternating between monism and 

 dualism according as it saw fit to sacrifice opposition 

 to unity or unity to opposition. 



But Hegelianism rejects neither; rather does it 

 preserve both in the synthesis of a third. Unity for 

 it is a matter of congruence such as we have in plane 

 geometry when two triangles which are alike except 

 for a reverse order of parts are brought into coin- 

 cidence. Wherever we find symmetry of structure, 

 there is a dualism of opposites and symmetry is, 

 as we have seen, a fourth-dimensional phenomenon. 

 Is not the turning of an object into its mirror image 

 a coincidence of opposites? Yet such a rotation 

 about a plane in the fourth dimension is the mere 

 analogue of the rotation in our three-dimensional 

 space about a line. 



When we have learned to think those states of con- 



